Variability in a Model of Divergent and Convergent Coupled Ice Streams: Synchronisation, Transients and Chaos
Abstract
Fast-flowing glaciers, known as ice streams, control the majority of ice sheet mass loss due to thermomechanical coupling at their base, which can induce basal lubrication and highly variable flow. Even quite simple models can show `binge-purge' oscillations. Recent work has highlighted that coupling between divergent ice streams can also give rise to chaotic variability. In this paper, we return to a model of ice streams with a divergent coupling to identify and correct some physical inconsistencies, most notably a global volume conservation error. We propose and validate a revised Divergent Coupling (DC) model that ensures rigorous mass balance. Bifurcation analysis and Poincaré sections reveal previously unidentified complex frequency-locking (Arnold tongues), a period-adding cascade and chaos associated with torus breakdown. We also consider an equivalent model with a Convergent Coupling (CC), where we find no evidence of chaotic variability. These findings suggest the importance of specific topologies on ice stream variability.
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BibTeX
@misc{grimstead2026variability,
title = {{Variability in a Model of Divergent and Convergent Coupled Ice Streams: Synchronisation, Transients and Chaos}},
author = {Joshua Grimstead and Peter Ashwin and Tanja I. Schindler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12246},
eprint = {2609.12246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12246},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Variability in a Model of Divergent and Convergent Coupled Ice Streams: Synchronisation, Transients and Chaos
AU - Joshua Grimstead
AU - Peter Ashwin
AU - Tanja I. Schindler
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12246
UR - https://arxiv.org/abs/2609.12246
AB - Fast-flowing glaciers, known as ice streams, control the majority of ice sheet mass loss due to thermomechanical coupling at their base, which can induce basal lubrication and highly variable flow. Even quite simple models can show `binge-purge' oscillations. Recent work has highlighted that coupling between divergent ice streams can also give rise to chaotic variability. In this paper, we return to a model of ice streams with a divergent coupling to identify and correct some physical inconsistencies, most notably a global volume conservation error. We propose and validate a revised Divergent Coupling (DC) model that ensures rigorous mass balance. Bifurcation analysis and Poincaré sections reveal previously unidentified complex frequency-locking (Arnold tongues), a period-adding cascade and chaos associated with torus breakdown. We also consider an equivalent model with a Convergent Coupling (CC), where we find no evidence of chaotic variability. These findings suggest the importance of specific topologies on ice stream variability.
ER -